Take a story's temperature by studying its tone. Is it hopeful? Cynical? Snarky? Playful?
Cynical, Morose, Edgy
If this play were a person, it would be a person with a lot of mood swings.
One minute we're at a fancy feast with the most amazing food and entertainment you've ever seen, and the next minute, we're stuck in the middle of a tornado of rage and misanthropy. The good times we see in the first few scenes quickly give way to some really depressing events: Timon literally goes off into the woods to die alone; Alcibiades takes down his own city; merchants and Senators try to swindle Timon out of everything he has (and then some); and Apemantus is even grumpier than usual.
Once Timon jets off into the woods, the play becomes sarcastic and cynical about pretty much everything—especially humans. The mocking snark-fests between Timon and Apemantus create an edgy quality to the play: we get the sense that a lot of what they're saying is actually supposed to be about Shakespeare's London, not ancient Athens. Maybe Timon's really looking at you, King James I.
We'd also like to point out that maybe the tone changes a bunch in the play because Shakespeare co-wrote it with Thomas Middleton. When the play shifts from one playwright to the other, so does the tone.